In DE 195 39 607 A1 such a bulletproof glass window for a motor vehicle is described. The known bulletproof glass window is manufactured as a laminated glass pane made of several glass layers or glass panes, eight in all, with the circumferential edge of one of the glass panes jutting out beyond the other glass panes along the edge of the bulletproof glass window, thus forming a projection. Between the surfaces of the glass panes, which are identical in area, are connecting layers made of polycarbonate film that join the glass panes together. The bulletproof glass window is mounted in a window frame of the car body at the projection, i.e. the protruding section of the glass pane that juts out, the mounting being provided on the glass surfaces of the projection. In the direction of the interior of the motor vehicle, the known bulletproof glass window has a grading or stepped portion from the protruding section to the faces or front surfaces of the following glass panes. Practical tests, however, in particular crash tests, have shown that from the area of the protruding section glass splinters can be projected into the interior of the motor vehicle, creating a potential danger to passengers in the motor vehicle.